ADC Energy Efficiency: Nyquist vs. DSM

ADC ENERGY EFFICIENCY: As a complement to the previous post, the energy vs. resolution is compared for Nyquist ADCs and ∆∑-modulators (DSM) in this post.

Class differences

Although it’s good to get an overall view of the landscape first, the previous post didn’t reveal any detail other than the basic shape, and the state-of-the-art border or envelope. We can get additional insight if we divide the data set by A/D-converter class. Every converter has been sorted into one of five classes:

Asynchronous

∆∑-modulator

Nyquist

Narrow-band

Other

Asynchronous means truly asynchronous, and does not include ADCs where the input is synchronously sampled and only the conversion is self-timed or ripple-through. Narrow-band is any converter other than ∆∑ for which the dynamic performance was calculated over a bandwidth lower than fs/2. Other is obviously the catch-all class for anything that didn’t fit in the other four.

Nearly all the data is in the DSM and Nyquist classes, so I have only used those two classes to render the Es vs. ENOB plot in Fig. 1. The global envelope is entirely defined by DSM and Nyquist converters. The envelope corner points [1]-[6] from the previous post are still annotated with first-author names, and a few more that are interesting for this discussion have been added as well [8]-[14].

As you can see from Fig. 1, the two state-of-the-art envelopes have very similar overall form: The energy seems to be limited by thermal noise constraints at higher resolutions, and they both level out to a constant Es, or at least a curve with much less slope at lower resolutions.

The main difference is that the DSM envelope defines the global state-of-the-art at high resolutions, and Nyquist converters define it for low to medium resolution. The transition point is currently at 12-b ENOB. Power-efficient ∆∑-modulators seem to have a noise-limited energy per sample from the 22-b ENOB reported by Naiknaware [6] down to the 12 bits reported by Shu [14]. Below 12 bits, the envelope quickly shifts to a much weaker dependency of resolution – not unlike the plateau observed in the previous post.

In comparison, the best Nyquist ADCs follow the thermal-noise energy model (or a slightly steeper slope) from the 15-b ENOB reported for SAR ADCs by Leung [7] and Hurrell [8] to the SAR ADCs reported by Harpe [4] and Liou [3] with 10 and 9-b ENOB, respectively. Below 9-b, I consider the envelope to be almost constant, as discussed in the previous post.

I guess you all observed the keyword SAR in the above paragraph, didn’t you? The SAR architecture defines more or less the entire shape of the Nyquist envelope, even if there are additional architectures along the plateau.

Energy bounds for low-resolution DSM

I hope there will soon be a theoretical analysis like [15] and [16] for ∆∑ too (please let me know if there is one already). Until then, we have to resort to empirical data. As briefly discussed in the previous post, it’s interesting to understand why the envelope breaks away from the thermal noise limit in the way it does, also for DSM. Are we looking at the same matching/min-size limits as suggested in a comment to the previous post. Lack of data? Lack of the “right” attempts? Limited expectations or other psychological barriers?

Since ∆∑-modulators are often viewed as “high-resolution”, I wanted to investigate the possible scarcity of data below the 12-b breakpoint around Shu [14]. Figure 2 shows how the highest ENOB reported in each paper distributes in the underlying data set. Eyeballing the histogram suggests that maybe as much as 40% of the DSM publications report a peak ENOB < 12-b, so “lack of attempts” can probably not explain why the envelope appears to degrade so quickly.

Fig. 2. Distribution of peak ENOB per scientific paper.

It is beyond the scope of this post to go really deep into the possible reasons for the “plateau-ish” low-resolution region for DSM, but I may return to investigate the composition of experimental data further to see if it can shed some light. For this post I mainly intended to show what the empirical data looks like. I also want to highlight two additional features of the DSM plateau:

Es is 1–2 orders of magnitude higher than for Nyquist converters.

The low-resolution envelope is defined by more unusual circuit implementations: Modulators presented by Daniels [13], Wismar [11] and Kim [10] are all VCO-based, whereas Chen [12] used a passive ∆∑-loop where only the comparator is active.

Why the 10–100X difference to Nyquist converters, then? From what I can see, most of the Nyquist converters that populate the low-energy envelope are the result of going to great lengths to weed out anything that has static current, and anything that switches faster or more often than it has to. Since the very foundation of oversampling is to evaluate the circuit state much more often than the Nyquist sampling rate, I assume it will be difficult to close the gap between these two envelopes.

But that’s me. Perhaps you have some idea how it could be done, or how to prove it isn’t possible?

As always, you are welcome to share your own thoughts and interpretations of the data.

Further reading

If you are curious to see what a more detailed breakdown by architecture would look like, you may find the plot in [17] interesting. Beware, though, that the data used in [17] does not include the most recent 400 or so papers from the last three years. Also, the plot is no masterpiece of readability 😉

3 responses to “ADC Energy Efficiency: Nyquist vs. DSM”

From your final comment, what happens if you take into account the oversampling factor of the DSM? (i.e. assuming all static power is gone, the capacitors switching are minimized and thermal noise is not limit, additional switching power due to OSR should worsen DSM).

For example, what happens if you calculate a FoM where for all types of ADCs you use 2xfB instead of fs? It’s somehow meaningless, but it could further point out to the oversampling being useful only for resolutions >12bits by trading it off with noise.

I hope it makes sense…

In any case congratulations for the blog posts and for sharing your insights